Archimedes
and genius of Archimedes, and it contains some precious details of the history of Greek astronomy which, coming from such a source and at first hand, posses
to exceed its multitude. And it is clear that they who hold this view, if they imagined a mass made up of sand in other respects as large as the mass of the earth, including in it all the seas and the hollows of the earth filled up to a height equal to that of the highest of the mountains, would be many times further still from recognising that any number could be expressed which
Aristarchus of Samos brought out a book consisting of some hypotheses, in which the premises lead to the conclusion that the universe is many times greater than that now so called. His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun in the circumference o
dence that the Greeks, in the person of Aristarchus of
to assume a definite size, however large, for the universe. Consequently he takes a liberty with Aristarchus. He says that the centre (a mathematical point) can have no ratio whatever to the surface of the sphe
he moon, and his own father, Phidias, had made it twelve times, while Aristarchus had tried to prove that the diameter of the sun is greater than eighteen times but less than twenty times the diameter of the moon (this was in the treatise of Aristarchus On the Sizes and Distances of the Sun and Moon, which is still extant, and is an admirable piece of geometry, proving rigorously, on the basis of certain assumptions, the result stated). Archimedes again intends to be on the safe side, so he takes the diameter of the sun to be thirty times that of the moon and not greater. Lastly, he says that Aristarchus discovered that the diameter of the sun appeared to be about 1?720th part of the zodiac circle, i.e. to subtend an angle of about half a degree; a
ircle is more than 3 times the length of the diameter of the circle, it easily follows that, while the diameter of the earth is less than 1,000,000
contains not more than 10,000 grains, and that the diameter of a poppy-seed is
he alphabetic system of numerals to express such large numbers as are required.
inning with 100,000,00099,999,999 and ending with 100,000,000100,000,000, which for brevity we will call P. Let all the numbers of all the orders up to P form the first period, and let the first order of the second period begin with P and end with 100,000,000 P; let the second order begin with this, the third order with 100,000,0002 P, and so on up to the 100,000,000th order of the second period, ending with 1,000,000,000100,000,000 P or P2. The first order of the third period beg
eyond the eighth order of the first period. The orders of the first period begin respectively with 1
multiplies the diameter of the sphere continually by 100, and states the corresponding number of grains of sand. A sphere of diameter 10,000 dactyli and a fortiori of one stadium contains less than 1021 grains; and proceeding in this way to spheres of diameter 100 stadia, 10,000 stadia and so on, he arrives at the number of grains of sand in a sphere of diameter 10,
Romance
Romance
Romance
Billionaires
Romance
Xuanhuan